Math Problem Statement
What is the variance of the stock's returns? Var(R) = 1/4-1 x [(-0.0455-0.1033)^2+(0.2852-0.1033)^2+(0.1261-0.1033)^2+(0.0473-0.1033)^2] The variance of the stock's returns is enter your response here. (Round to five decimal places.)
Solution
as np
Given values for the calculation
returns = [-0.0455, 0.2852, 0.1261, 0.0473] mean_return = 0.1033
Variance formula calculation
variance = (1 / (4 - 1)) * sum((x - mean_return) ** 2 for x in returns)
Round to five decimal places
variance_rounded = round(variance, 5) The variance of the stock's returns is 0.01963.
Would you like a detailed explanation or have any questions? Here are some related questions to deepen your understanding:
- How is variance used to measure the risk of a stock's returns?
- What is the difference between variance and standard deviation in financial contexts?
- How would the variance change if additional data points were added?
- Can you explain why dividing by (instead of ) is used in this calculation?
- How does the mean return affect the calculation of variance?
Tip: Variance provides a good measure of dispersion but interpreting it alongside the mean return is crucial for investment decisions.
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Math Problem Analysis
Mathematical Concepts
Statistics
Variance Calculation
Mean and Dispersion
Formulas
Variance = (1 / (n - 1)) × Σ(x_i - mean)^2
Theorems
Central Limit Theorem (implicitly relevant when interpreting statistical measures)
Suitable Grade Level
Grades 10-12
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